This application is related to co-pending U.S. patent application entitled xe2x80x9cSystem and Method for Rapidly Generating an Optimal Mesh Model of a 3D Object or Surfacexe2x80x9d filed on even date herewith. The co-pending application is expressly incorporated herein by reference.
1. Field of the Invention
This invention relates to computer systems for three-dimensional (xe2x80x9c3Dxe2x80x9d) modeling of real-world objects, terrains and other surfaces. In particular, this invention relates to computer systems which create optimized mesh models of objects and surfaces and have the capability to change dynamically the construction of the model to represent the object or surface in varying levels of detail.
2. Background of the Invention
There is great interest in the development of computer systems which enable users to generate quickly accurate displays and reproductions of real world objects, terrains and other 3D surfaces. A graphic display and manipulation system generates a mesh model of the object, terrain or surface, uses that mesh model as a basis to create the display or reproduction and allows the user to manipulate the model to create other displays such as xe2x80x9cmorphs,xe2x80x9d fantasy displays or special effects. A mesh model represents an object, terrain or other surface as a series of interconnected planar shapes, such as sets of triangles, quadrangles or more complex polygons. More advanced graphic display systems provide rapid zoom and xe2x80x9cwalk aroundxe2x80x9d capabilities (allowing the viewer to make his or her perceived vantage point appear to move closer to, farther from or about an object or surface). The mesh modeling of these systems must be flexible and provide dynamic resolution capabilities as well as display a high quality reproduction of the object.
A set of data points that describes the object or surface provides basic data for the mesh. The data points represent actual, measured points on the object, surface or terrain. Their values come from a number of sources. A user can input data points based on measurement or planned architecture or they can be generated through scanning and other measuring systems. A scanning system uses a light source such as a laser stripe to scan and a camera to collect images of the scanning light as it reflects from the object. A scanning system processes the information captured in the images to determine a set of measured 3D point values that describe the object, surface or terrain in question. Scanning systems can easily gather the raw data of several hundred thousand 3D coordinates. The data points come to the mesh modeling system as a group of randomly distributed points. Other data concerning the object, terrain or surface, such as a texture map, ambient light data or color or luminosity information, can be associated or used in conjunction with the geometric shapes of the mesh.
Typical mesh modeling systems use data points either indirectly (in gridded network models) or directly (in irregular network models) to create meshes. U.S. Pat. No. 4,888,713 to Falk and U.S. Pat. No. 5,257,346 to Hanson describe ways of creating gridded mesh representations. Gridded network models superimpose a grid structure as the basic framework for the model surface. The grid point vertices form the interconnected geometric faces which model the surface. The computer connects the grid points to form evenly distributed, geometric shapes such as triangles or squares, that fit within the overall grid structure. While gridded models provide regular, predictable structures, they are not well suited for mesh construction based on an irregular, random set of data points, such as those generated through laser scanning (as mentioned above). To fit the irregular data points of a laser scan into a rigid grid structure, the data point values must be interpolated to approximate points at the grid point locations. The need to interpolate increases computation time and decreases the overall accuracy of the model.
Compared to a gridded model, an irregular mesh model provides a better framework for using irregular data points, because the irregularly-spaced data points themselves can be used as the vertices in the framework, without the need to interpolate their values to preset grid point locations. A typical irregular network meshing system builds a mesh by constructing edge lines between data points to create the set of geometric faces that approximate the surface of the object or terrain. There has been widespread interest in building irregular mesh models having planar faces of triangular shapes, as only three points are needed to determine a planar face.
While irregular triangular meshes offer the possibility of more accurate displays, the systems to implement them are more complex compared to gridded network models. The limitations of the computer hardware and the complexity inherent in the data structures needed for implementation of irregular mesh building systems has prevented their widespread use. U.S. Pat. No. 5,440,674 to Park and U.S. Pat. No. 5,214,752 to Meshkat et al. describe meshing systems used for finite element analysis, i.e., the partitioning of CAD diagrams into a series of mesh faces for structural analysis, not the creation of a mesh from a series of raw data points. Further, these systems do not permit dynamic variable resolution. To alter the resolution of the meshes in these systems, the operator must reinitiate and recreate the entire mesh. As such, the systems do not appear suitable for the dynamic mesh generation requirements of applications such as computer animation and special effects.
For computer mesh applications involving the hundreds of thousands of 3D data points typically used in computer animation, there is a need for the creation of a mesh system which can generate a mesh with substantial speed and rapidly vary its resolution. Speed and data storage requirements are also important factors in graphic display applications on communication systems such as the Internet. Currently, Internet graphic displays are typically communicated as massive 2D pixel streams. Each and every pixel displayed in a 2D image must have a pixel assignment. All of those pixel assignments must be transmitted via the communications system. Such a transmission requires large amounts of communication time. Further, if movement is depicted in the display, information must be continuously sent over the communications system to refresh the image or, in the alternative, one large chunk of pixel data must be downloaded to the receiving terminal before the display can begin. Replacing the 2D image display system with a 3D modeling system substantially reduces the amount of data needed to be transmitted across the communication system, because with a 3D modeling system only representative 3D data points need be sentxe2x80x94not a full set of assignments for every pixel displayed. A mesh generating system located at the receiver terminal could generate a full display of the object upon receiving relatively few 3D data points. Currently available meshing systems do not provide this capability.
The demands of computer animation and graphic display also call for improvement in the quality of the mesh. In the case of an irregular triangulated mesh, for example, when the angles of one triangle""s comers vary widely from the angles of another triangle or the triangles differ wildly in shape and size, the mesh tends to be difficult to process for functions such as xe2x80x9cgluingxe2x80x9d (joining a mesh describing one part of an object to a mesh describing an adjacent part). Such a mesh will also display badly. For example, a non-optimized triangulated mesh might show a jagged appearance in the display of what are supposed to be smooth curving surfaces like the sides of a person""s face. Generally, an underlying mesh model constructed from small, regularly angled triangles that tend towards being equilateral is preferable.
The procedure of B. Delaunay known as xe2x80x9cDelaunay Triangulationxe2x80x9d is one optimization theory which researchers have attempted to implement for the construction of a high quality, irregular meshes with homogeneous triangular structure. Delaunay""s theories for the creation of irregular mesh lattices derive from the teachings of M. G. Voronoi and the studies he made of xe2x80x9cVoronoi polygonsxe2x80x9d. Voronoi determined that, for a set of data points in space, a proximity region could be defined for each data point by a convex polygon created from the perpendicular bisectors of lines drawn from the point in question to its nearest neighbors. FIG. 1a shows an example of a Voronoi polygon. Each data point is bounded by a unique Voronoi polygon created through those bisecting lines. The edges of each Voronoi polygon are shared with Voronoi polygons for the interconnected points. Thus, Voronoi""s method describes a surface with a series of unique, complex polygons. FIG. 1b depicts an example of a Voronoi polygon diagram.
Delaunay""s theories follow the teachings of Voronoi and seek to create an irregular triangulated mesh with a tendency for homogeneous triangles. It has been proven that every vertex of a Voronoi diagram is the common intersection of exactly three polygonal edges. Equivalently, it has been proven that each vertex of a Voronoi polygon is a center of a circle defined by three of the data points bounded by the Voronoi polygons. See, e.g., Computational Geometry, Preparata and Shamos, New York, Springes-Verlag, 1988 (second printing). From those observations, it is possible to create from any Voronoi diagram a xe2x80x9cstraight-line dualxe2x80x9d diagram having similar properties. FIG. 1c depicts a straight line dual diagram made from the data points bounded by the Voronoi polygon in FIG. 1b. Notice that the xe2x80x9cstraight-line dualxe2x80x9d is a triangular mesh constructed using the actual data points, not the vertices of the Voronoi polygons created by the bisecting lines. The straight-line dual diagram forms its triangular mesh shape by constructing straight line segments between each pair of data points whose Voronoi polygons share an edge. (See FIG. 1c.) It has been proven that a straight line dual of a Voronoi diagram always produces an irregular triangulated mesh. Ibid.
Delaunay used the Voronoi straight line dual to create triangulated lattices with properties derived from an understanding of the Voronoi polygonal diagram. When a triangulation follows Delaunay principles, a circumcircle defined by the vertices of a triangle will not contain another data point of the mesh. FIG. 1d depicts a circumcircle for determination of whether the triangle meets the Delaunay optimality criteria. A Delaunay mesh procedure guarantees that for each triangle of the mesh the area within a circumcircle created from the three vertices will not contain any other data point of the mesh.
Research shows that a triangulated mesh which adheres to the Delaunay circumcircle principle yields an optimized mesh which behaves well in display and graphic manipulations systems. However, Delaunayian meshing procedures, such as those described by Park and Meshkat, for example, do not operate at high speed to build a mesh from a large set of raw data points and they do not provide dynamic resolution. The few currently available meshing procedures which even attempt to optimize Delaunay theories use slow recursive means that rely on time-consuming parameter passing and checking steps. Such problems have stifled the use of real-life object depictions in computer graphics applications.
Therefore, it would represent a substantial advance in the field if a computer modeling system could be developed that allows for rapid generation of a mesh optimized by principles such as those set forth in the theories of Delaunay and Voronoi and provide dynamic resolution capabilities. Such a system would enable computer graphics systems to use real world images in all applications, including multi-resolution displays. The system would enable communication systems, such as the Internet, to display and manipulate images and models of the real world objects more rapidly.
The present invention provides a system and method for rapid computer creation of an optimal mesh with dynamic resolution capabilities. The mesh building system and method operates incrementally, building the mesh point-by-point in succession. As each point is added, optimality is preserved through a rapid, non-recursive checking procedure. In an exemplary embodiment, the system of the present invention creates a triangulated mesh, optimized by Delaunay principles. Each point is added to the mesh by linking it to other related points. Once the system establishes an initial Delaunay triangulated mesh, new points may be added quickly. First, the system locates the triangle or area in the existing mesh into which the next point will be added. Next, the system splits this triangle into three triangles, each containing two vertices of the original triangle and the new vertex. The links between the old vertices and the new point form the geometric edges of the triangle. Next, the system checks each triangle in the neighborhood around the insertion point, reconstructing if necessary to maintain an optimal triangulation such as a Delaunay triangulation. One particular advantage of the system is the speed at which it operates in mesh building and checking. The system operates in order (n log n) time and can provide a full mesh of 100,000 data points in xcx9c1.7 seconds operating on a 195 MHZ R10000 processor.
One aspect of the system and method of the present invention is the processing of the data points before insertion. This processing allows for dynamic resolution (up resolution/down resolution) capabilities in the level of detail for the mesh created. In placing the points into the mesh, the present invention teaches that the data points can be ordered such that the first few points (10-50, depending on the object) describe the overall basic shape of the object and each successive point adds increasing detail to that basic shape. The system and method of the present invention provides a detailed ordering routine which guarantees that each next point adds the most significant detail to the mesh compared to all remaining unmeshed points. This ordering permits dynamic xe2x80x9cup resxe2x80x9d or xe2x80x9cdown resxe2x80x9d mesh construction. To increase resolution, the system adds points to further increase detail. To decrease resolution the system removes the later added points of fine detail before removing the points showing basic detail. At any given increment in the point addition process, the mesh will always have the simplest depiction of the object and contain the most significant points in terms of descriptive detail. The remaining unmeshed points will all be points which add more refined detail compared to those already in the mesh. Thus, the present invention guarantees an optimal, simplified mesh in any configuration. The procedure can be referred to as xe2x80x9coptimal simplification.xe2x80x9d
To maintain optimal simplification, the present invention provides a set of data structures and program elements to manage the ordering and incremental insertion of data points. In an exemplary embodiment, the distance each unmeshed point has in relation to the surface of a given mesh configuration determines the order of significance. As points are added or deleted, the configuration of the mesh changes and, for the remaining unmeshed points, the order of significance must be redetermined. The present invention provides a system for continuously ordering the unmeshed points so that the next most significant point is always identified. The system maintains speed in reordering by identifying after each insertion or deletion the unmeshed points that are affected by the change and performing reevaluation calculations only on those affected points.
To insert a new data point into the mesh, a set of computer program elements and data structures enable a computer processor to implement a series of changes. An inserted point creates additional mesh faces. The inserted point may also require alterations of the edges of the faces to preserve optimality. The system rigidly orders the vertices of the new triangular faces created by the inserted point. In an exemplary embodiment, the vertices of the triangles are ordered in counterclockwise fashion. However, a clockwise or other rigid ordering system is also suitable. The edges of the newly created triangles and the neighboring triangles related to those edges are also ordered in relation to the counterclockwise or other ordering of the vertices of each face. The present invention performs optimality checks in a systemized way, moving in a single direction following the ordering of the points, such as proceeding counterclockwise around the insertion point. The regularized indexing of the vertices (in the counterclockwise or other order) enables the checking procedure to easily orient itself within the mesh and quickly maneuver to check for optimized quality.
As each face is checked, the present invention provides that the results of each check be stored in a history list data structure. The system and method of vertex indexing and the system and method of regularized checking enables the present invention to store only minimal information about the checking. The minimal storage requirements allow for application of the present invention on communication systems like the Internet. The history list is used during point removal to reverse the mesh construction steps that occurred when the data point was inserted. In the present invention, data points are added and deleted from the mesh in LIFO (last in first out) order, thereby keeping the points of most significant detail in the mesh at all times. A data structure maintains a list of inserted points. This list is used in conjunction with the history list to remove points or quickly replicate the mesh in differing levels of detail.
As stated above, the present invention provides a checking process that works in a sequenced, step-wise manner to implement an optimization heuristic such as a Delaunay triangulation. It is an aspect of this invention that a mesh of optimal quality is maintained at all times, even in dynamic up res/down res construction. Delaunay principles dictate that a circumcircle created by the vertices of any mesh triangle will not contain any other data point. If the triangle does not pass that test, then it is not considered optimal and the edges between the vertices must be redefined or xe2x80x9cflippedxe2x80x9d to create a new set of triangles. The system insures that the vertices and neighbor relationships of the flipped triangles also allow for the sequenced checking.
After flipping, the system and method of the present invention continues to check for optimization, rechecking the flipped triangles and their neighbors and storing the results of that checking on the history list. The present invention teaches that an entire triangulation check must take place in an ordered fashion, such as a counterclockwise or other order as described above. If an ordered system of checking is maintained, and the results are known through the history list, the system can rapidly remove points to provide down resolution capabilities by reversing the system of mesh alterations and removing the added points in LIFO order.
The history file can be used for dynamic up resolution to gain substantial speed increases. After one mesh is built to full resolution using the point ordering and optimality procedures outlined above and collecting the record of the changes in the history list, the mesh can be almost instantaneously generated to any detail level, using the history file instead of reexecuting the ordering and checking procedures. Although building the mesh and storing the changes in the history list increases processing time for an initial mesh (by approximately 13%), the system can mesh with very high speed once the history list has been created. For a cache of 100,000 points in a 195 MHZ R10000 processor, the surface meshes at 700,000 triangles/second. For a cache of 25,000 data points, the system meshes at a speed of 750,000 triangles/second . For a cache of 4,000 data points, the system can mesh at a speed of 1,250,000 triangles/second. The speed will vary depending on the size of the data cache permitted for the data points in the computer system.
The system and method of the present invention comprises computer hardware, programmed and data structure elements. All the elements set forth are described in more detail below.